A uniform rod of mas m and length l is kept vertical with the lower end clamed. It is slightly pushed to let it fall down under gravity. Find its angular speed when the rod is passing through its lowest positon. Neglect any friction at the clamp. What will be the linear speed of the free end at this instant?

Explanation

To solve the problem of finding the angular speed of a uniform rod when it is passing through its lowest position and the linear speed of the free end at that instant, we can follow these steps:

### Step 1: Understand the System
A uniform rod of mass \( m \) and length \( l \) is clamped at one end and allowed to fall under the influence of gravity. When it falls, it rotates about the clamp at the bottom.

### Step 2: Apply the Work-Energy Theorem
According to the work-energy theorem, the work done by gravity on the rod will equal the change in kinetic energy of the rod. The work done by gravity can be calculated as:
\[
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